Imbeddings into groups of intermediate growth

Abstract

Abstract. Every countable group that does not contain a finitely generated subgroup of exponential growth imbeds in a finitely generated group of subexponential word growth.

Matrix wreath products of algebras and embedding theorems

“…Neumann [11] proved that every countable group embeds in a finitely generated group. The papers [3], [20], [21], [22], [24] show that some important properties can be inherited by these embeddings. Much of this work relies on wreath products of groups.…”

Embeddings in Lie algebras of subexponential growth

“…A. I. Malcev [5] and A. I. Shirshov [6] proved analogous results for countable dimensional associative and Lie algebras respectively. In [3] L. Bartholdi and A. Erschler showed that an arbitrary countable group that is locally of subexponential growth is embeddable in a finitely generated group of subexponential growth. The key role in their construction was played by wreath products with the infinite cyclic group.…”

Algebras and semigroups of locally subexponential growth

“…The proof of Theorem 1 is based on a new construction of the matrix wreath product A ≀ F [t −1 , t]. We view it as an analog of the wreath product of a group G with an infinite cyclic group Z that played an essential role in the Bartholdi-Erschler proof [2].…”

“…The papers [9], [10], [11], [13] show that some important properties can be inherited by these embeddings. In the recent remarkable paper [2], L. Bartholdi and A. Erschler proved that a countable group of locally subexponential growth embeds in a finitely generated group of subexponential growth.…”